# Averaging bias correction for the future space-borne methane IPDA lidar mission MERLIN

The CNES (French Space Agency) and DLR (German Space Agency) project MERLIN is a future integrated path differential absorption (IPDA) lidar satellite mission that aims at measuring methane dry-air mixing ratio columns (inline-formula $M1inlinescrollmathml{X}_{chem{\mathrm{normal CH}}_{normal 4}}\right)$ 29pt15ptsvg-formulamathimg51672dd6e6383a0f770a00cc11c13f64 amt-11-5865-2018-ie00001.svg29pt15ptamt-11-5865-2018-ie00001.png in order to improve surface flux estimates of this key greenhouse gas. To reach a 1 % relative random error on inline-formula $M2inlinescrollmathml{X}_{chem{\mathrm{normal CH}}_{normal 4}}$ 24pt14ptsvg-formulamathimgfc9460dd9869759f9331ac4e22ef11e2 amt-11-5865-2018-ie00002.svg24pt14ptamt-11-5865-2018-ie00002.png measurements, MERLIN signal processing performs an averaging of data over 50 km along the satellite trajectory. This article discusses how to process this horizontal averaging in order to avoid the bias caused by the non-linearity of the measurement equation and measurements affected by random noise and horizontal geophysical variability. Three averaging schemes are presented: averaging of columns of inline-formula $M3inlinescrollmathml{X}_{chem{\mathrm{normal CH}}_{normal 4}}$ 24pt14ptsvg-formulamathimg8965335be9e41dc029807579a00c466b amt-11-5865-2018-ie00003.svg24pt14ptamt-11-5865-2018-ie00003.png , averaging of columns of differential absorption optical depth (DAOD) and averaging of signals. The three schemes are affected both by statistical and geophysical biases that are discussed and compared, and correction algorithms are developed for the three schemes. These algorithms are tested and their biases are compared on modelled scenes from real satellite data. To achieve the accuracy requirements that are limited to 0.2 % relative systematic error (for a reference value of 1780 ppb), we recommend performing the averaging of signals corrected from the statistical bias due to the measurement noise and from the geophysical bias mainly due to variations of methane optical depth and surface reflectivity along the averaging track. The proposed method is compliant with the mission relative systematic error requirements dedicated to averaging algorithms of 0.06 % (inline-formula±1 ppb for inline-formula $M5inlinescrollmathml{X}_{chem{\mathrm{normal CH}}_{normal 4}}=normal 1780\phantom{\rule{0ex}{0ex}}\mathrm{normal ppb}$ 82pt14ptsvg-formulamathimgc59bc757b8bd434c78894f59a5f23122 amt-11-5865-2018-ie00004.svg82pt14ptamt-11-5865-2018-ie00004.png ) for all tested scenes and all tested ground reflectivity values.

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Tellier, Yoann / Pierangelo, Clémence / Wirth, Martin / et al: Averaging bias correction for the future space-borne methane IPDA lidar mission MERLIN. 2018. Copernicus Publications.

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